Question

I was wondering how to find these things about the Singapore flyer(ferries wheel)? The measure of the central angle in degrees, the measure of the central angle in radian, the arc length between two cars, and the area of a sector between two cars?

Answer 1

Well you need to know 2 things: the number of cars and the radius of the wheel.

Angle in degrees = 360 / number of cars.
Angle in radians = 2π / number of cars.
Arc length = angle in radians * radius.
Area sector = 1/2 * arc length * radius.

Answer 2

Answer:

1)$\alpha =\frac{S}{r}$S in degrees 2)$\alpha =\frac{S}{r}$ S in radians 3)$S=r*\alpha$ 4)$S=\pi r^{2} \frac{\alpha }{360}$ (degrees) $S=\pi r^{2} \frac{\alpha }{2\pi}$ (radians)

Step-by-step explanation:

Hi there, since you've mentioned a Ferris wheel. It's important have at hand some important formulas. To measure the central angle, we derive it from this formula:

1)The measure of the central angle in degrees:

For this, we need to have a defined arc. Then we can find a central angle of this arc. Notice the unit must be in degrees for the arc.

$S=r*\alpha \\ \frac{S}{r}=\frac{r\alpha }{r}\\  \frac{S}{r}=\alpha$

S= arc length (an arc from the Ferris Wheel) in degrees

r=radius

2)The measure of the central angle in radians

For this, we need to have a defined arc. Then we can find a central angle of this arc. Notice the unit must be in radians for the arc.

$S=r*\alpha \\ \frac{S}{r}=\frac{r\alpha }{r}\\  \frac{S}{r}=\alpha$

S= arc length (an arc from the Ferris Wheel) in Radians

r=radius

3) The arc length between two cars

This is any arc at the Ferris Wheel. Therefore, we can use this same formula. Since the distance between two cars define an arc.

$S=r*\alpha$

4) And the area of a sector between two cars

But if you want the area of the circular sector, is given by this formula below if you want it in degrees

$S=\pi r^{2} \frac{\alpha }{360}$

And in that, if you want it in radians:

$S=\pi r^{2} \frac{\alpha }{2\pi}$